हिंदी

The Number of Permutations of N Different Things Taking R at a Time When 3 Particular Things Are to Be Included Isn − 3pr − 3,N − 3pr,Npr − 3,R ! N − 3cr − 3 - Mathematics

Advertisements
Advertisements

प्रश्न

The number of permutations of n different things taking r at a time when 3 particular things are to be included is

विकल्प

  • n − 3Pr − 3

  •  n − 3Pr

  • nPr − 3

  • r ! n − 3Cr − 3

MCQ
Advertisements

उत्तर

r ! n − 3Cr − 3

Here, we have to permute n things of which 3 things are to be included.
So, only the remaining (n - 3) things are left for permutation, taking (r - 3) things at a time. This is because 3 things have already been included.

But, these r things can be arranged in r! ways.
∴ Total number of permutations = r ! n − 3Cr − 3
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.7 [पृष्ठ ४६]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.7 | Q 1 | पृष्ठ ४६

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?


Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?


Which of the following are true:

(2 × 3)! = 2! × 3!


How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?


How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?


Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.


Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?


In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?


There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?


Evaluate each of the following:

8P3


In how many ways can 4 letters be posted in 5 letter boxes?


Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.


Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?


Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?


How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?


The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is


If (n+2)! = 60[(n–1)!], find n


In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?


Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.


Evaluate the following.

`(3! xx 0! + 0!)/(2!)`


Evaluate the following.

`(3! + 1!)/(2^2!)`


For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:


The number of ways to arrange the letters of the word “CHEESE”:


If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r


How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?


8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?


A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?


How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are together


Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are divisible by 4?


How many words can be formed with the letters of the word MANAGEMENT by rearranging them?


Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together


The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.


The total number of 9 digit numbers which have all different digits is ______.


The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.


Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find

C1 C2
(a) How many numbers are formed? (i) 840
(b) How many number are exactly divisible by 2? (i) 200
(c) How many numbers are exactly divisible by 25? (iii) 360
(d) How many of these are exactly divisible by 4? (iv) 40

If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.


If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.


The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×